1/16=64^(4x-3)
1/(4^2) = (4^3)^(4x-3) ... since 16 = 4^2 and 64 = 4^3
4^(-2) = 4^(3*(4x-3))
so because the bases are now the same, we can say that the exponents must be the same
so...
-2 = 3*(4x-3)
solve for x